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(c) Angle bisection using ruler and compass

Suppose we have to bisect ∠PQR.
l Place the compass pointer at point Q and make an arc that cuts the two arms of the angle
at two different points.
l From the points where the arc cuts the arms QP and QR, make two arcs towards the interior
of the angle so that the two arcs intersect each other at a point, say S.
l Join the point of intersection S to the vertex Q with a ruler.

Thus, QS is the angle bisector of ∠PQR.

Practice Time 2E

1. Using a protractor, draw angles with the following degree measures.
(a) 80° (b) 44° (c) 125°
(d) 187° (e) 156° (f) 195°
2. Draw an angle whose degree measure is the same as the angle given below.

Also, draw its angle bisector and write down the steps you followed.
3. Draw the letter ‘W’ such that the angles on the sides are 40° each, and the angle in the middle is 60°.
4. Copy the given angle onto a transparent sheet/tracing paper, and fold the sheet to get the angle bisector.

Verify your findings using a protractor.
5. Find the degree measures of ∠PQR, ∠PQS, ∠RQS and ∠PQT.

S
R

T
P

Q
(a) Is QS the angle bisector of ∠RQT?
(b) Is QR the angle bisector of ∠PQS?

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